Hanna (Sarah Polley), a solitary and mysterious young woman, works in a factory somewhere in Europe. She speaks to no one, eats the same thing for every meal and wears a hearing aid that she turns off to protect herself from the world. Forced by her boss to take a vacation, she travels to Northern Ireland where, on a whim, she volunteers to be a nurse on an oil rig in the Irish Sea to tend to Josef (Tim Robbins) who has been burned in a flash fire. The burns have left Josef temporarily blind but in flirtatious spirits and he is eager to discover who his enigmatic nurse truly is.
On the oil rig, Coixet creates a labyrinthine world where only a handful of other characters live, including Martin (Daniel Mays), an oceanographer who shoots balls into a basketball hoop and Simon (Javier Camara), the rig’s jovial cook who turns out gourmet meals for the crew.
As Hanna tends Josef's wounds, he attempts in vain to extract information about her all the while telling her about his own troubled past. Hannah even refuses to tell Josef her real name or the color of her hair. Yet, a strange intimacy gradually develops between them and when Josef is about to be transferred off the rig, Hanna knows they may never see each other again. She decides to divulge her darkest secret, a revelation from which neither will emerge unscathed and will change their lives forever.